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Storage and retrieval of two unknown unitary channels

Michal Sedlák1,2, Robert Stárek3, Nikola Horová3, Michal Mičuda3, Jaromír Fiurášek3, and Alessandro Bisio4,5,*

  • *Contact author: alessandro.bisio@unipv.it
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Phys. Rev. A 114, 032404 – Published 2 September, 2026

DOI: https://doi.org/10.1103/56sd-xw8b

Abstract

We address the task of converting n uses of an unknown unitary transformation into a quantum state (i.e., storage) and later retrieval of the transformation. Specifically, we consider the case where the unknown unitary is selected with equal prior probability from two options. First, we prove that the optimal storage strategy involves the sequential application of the n uses of the unknown unitary, and it produces the optimal state for discrimination between the two possible unitaries. Next, we show that incoherent “measure-and-prepare” retrieval achieves the maximum fidelity between the retrieved operation and the original (qubit) unitary. We then identify the retrieval strategy that maximizes the probability of successfully and perfectly retrieving the unknown transformation. In the regime in which the fidelity between the two possible unitaries is large the probability of success scales as Psucc=1−O(n−2), which is a quadratic improvement with respect to the case in which the unitaries are drawn from the entire unitary group U(d) with uniform prior probability. Finally, we present an optical experiment for this approach and assess the storage and retrieval quality using quantum tomography of states and processes. The results are discussed in relation to nonoptimal measure-and-prepare strategy, highlighting the advantages of our protocol.

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Phys. Rev. A 114, 032404– Published 2 September, 2026
  • Received 3 September 2025
  • Revised 12 May 2026
  • Accepted 25 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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